Out of the three, which is the best option and with which grammatical rule:
- I have four dozens of mango.
- I have four dozen of mangoes.
- I have four dozens of mangoes.
Hundred, thousand, pair, dozen, and couple take the same form both in the singular and in the plural only when they are used after numerals or after several or a few.
Three hundred (not hundreds), two pair, three couple, five dozen etc.
- He gave me a sum of three hundred rupees.
- He bought two pair of shoes.
- There are five dozen mangoes in the basket.
NOTE: In modern English, "pairs" and "couples" are more usual.
- He bought two pairs of shoes.
- Five couples were present at the meeting.
When the nouns of numbers are followed immediately by "of," their plural forms are used.
- Hundreds of people.
- Hundreds of thousands of people.
Based on that, the correct answer is #2:
- I have four dozen mangoes. or I have four dozen of mangoes.
- I have two pair of dresses.
But, we say:
- I have dozens of mangoes.
- I have a number of pairs of dresses.
Since many are concluding that using "of" is not correct, It is uncommon, but it is not wrong either, maybe to American/British, but It is very common to use "of" after "dozen" in India. Since the OP is Indian, I have provided a source from an Indian book.
But as you can see here, the results are very contrasting to the previous one:
Here is something that may help you: English Grammar without Tears
Assuming that what you have is 48 mangoes; you have four dozen mangoes.
The reason for this is that "four dozen" is a number. You wouldn't say "I have four of mango", "fours of mangoes" etc.
Use of dozen is, of course, an English oddity, but it does compare to the other units OK: So "I have four hundred mangoes" is the same construction.
The rule is simple. It depends on whether you're using `dozen' as an adjective or as a noun. Nouns can be singular or plural; adjectives are unit-less (as the noun that the adjective is qualifying carries the numerical dimension). So, the following are correct:
Dozens of mangoes were destroyed (what a pity!).
Give me a dozen ['of those' implied].
Four dozen mangoes were not destroyed (thank God!)
I have a few dozen shoes.
Similarly, we never say 'five thousands dollars', as we're using it as an adj.
Additionally, I'd like to point that 'pair' is not an adjective, but a noun.
NOTES FROM OED -
A group or set of twelve. Originally as a noun, followed by of, but often with the ellipsis of of, and thus in singular = twelve.
Also, used colloq. in plural, either indefinitely or hyperbolically, for any moderately large number.
Example sentences -
1. More than three dozen of President Obama's top fundraisers snagged VIP invites.
2. The owner receives 15 cents from the egg company for every one dozen of eggs produced.
3. He's written the music for half a dozen of actor and director Kenneth Branagh's films.
As the notes mentions the of after dozen is often dropped. And hence it's more common to use dozen like an adjective/determiner, with no of between dozen and the noun. You will see people hardly retain of, and some indeed object to the use of of there. Collins Cobuild Dictionary is one of them.
Many dictionaries categories dozen as adjective or determiner.
4. The author or co-author of two dozen books, Connery also taught more than four decades at universities including Stanford and Duke.
So what happens with sentences #1,#2 and #3. Are they incorrect?
No, the use of of there is fine. They are examples of partitive construction - some from a large group of things.
When dozens is used, it doesn't mean twelve, it means a large group of things. There is often an of between dozens and a noun.
5. But, first in Kuwait City, dozens of children and women are burned alive after a fire ripped through a packed wedding tent.
6. We collected dozens and dozens of shells on the beach.
7. The refugees arrived by the dozen/in their dozens.
Usage Note From MW Usage Dictionary -
Dozen has two plurals, a zero form dozen (just like the singular) and an inflected dozens. When a number is put before the noun, the zero form plural is used:
He that kills me some six or seven dozen of Scots - Shakespeare, I Henry IV, 1598
... stript away ten dozen Yards of Fringe —Jonathan Swift, A Tale of a Tub, 1710
... several million dozen pairs —B. Eldred Ellis, Gloves and the Glove Trade, 1921
... consuming... twelve dozen oysters, eight quarts of orange juice — Frank Sullivan, The Night the Old Nostalgia Burned Down, 1953
When the number is not specified, dozens is used:
... worked in dozens of minor roles in television plays — Current Biography, June 1965
Evans 1957 notes that of used to be common after dozen:
I bought you a dozen of shirts — Shakespeare, I Henry IV, 1598
... a dozen or so of people were sitting about — Archibald Marshall, Anthony Dare, 1923
This construction is now felt to be old-fashioned and is no longer used much. We do, of course, retain of after dozens:
Dozens of times since . . . I have been asked . . . — Joseph Wood Krutch, American Scholar, Spring 1955
It's correct to write the following -
He has bought four dozen mangoes.
Four dozen (of) mangoes were delivered from the storehouse.
There are dozens of mangoes scattered on the floor.